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Simple Answer:

When the driving force for convection is removed, the system will return to thermal equilibrium.

Explanation:

If convection exists in a fluid because a heat source is maintaining a temperature gradient and then that heat source is removed, the fluid will return to a stationary state with uniform temperature in a sequence of three overlapping stages.

1. With no driving force, the system initially continues the current flow and transport of heat, but the flow will slow and cease due to internal fluid viscosity

2. When system inertia of initial flow dissipates, new convection forces develop due to remaining thermal gradients and push fluid towards a configuration where density profile are perpendicular to gravitational forces.

3. Existing temperature gradients in the fluid will diminish through thermal conduction as the system proceeds toward a final uniform temperature.

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